Instability and Control of Massively Separated Flows

We study the stability of a jet in crossflow at low values of the jet-to-crossflow velocity ratio

$$R$$

R

focusing on direct numerical simulations (DNS) and the global linear stability analysis adopting a time-stepper method. For the simplified setup neglecting a meshed pipe in the simulations, we compare results of the fully-spectral code

SIMSON

with the spectral-element code

Nek5000

. We find the calculated critical value

$$R$$

R

for the first bifurcation to be dependent on the numerical method used. This result is related to a large sensitivity of the eigenvalues and to the large spatial growth of the corresponding eigenmodes, making the use of periodic domains, even with the fringe method, difficult. However, we observe a similar sensitivity to reflection from the outflow boundary in the inflow/outflow configuration as well. We apply in our studies both modal and non-modal analyses investigating transient effects and their asymptotic fate, and we find transient wavepacket that develop almost identically in the stable and unstable cases. Finally, we compare these results with the simulation including the pipe in the computational domain finding the latter one to be much more unstable.

Those working in the field of diagnostics continuously find new ways to visualise and quantify complicated flows in ways that were probably at some time thought to be impractical. These include either optimisation of already well-established techniques such as Schlieren with the development of higher resolution and faster cameras, or the invention of new methods by the synergy between different disciplines, such as pressure sensitive paints which bring together physics, chemistry and fluids. Ideally most of these diagnostic methods have a low parasitic profile or are completely non-intrusive. The present article paper gives a brief overview of some challenging investigations on shock boundary layer interactions using these flow diagnostic methods. A case study on axisymmetric transitional interactions at Mach 5 is also presented.

Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) are applied to the unsteady separated flow field over a NACA-0015 airfoil with periodic zero-net-mass-flux (ZNMF) jet forcing at the leading edge at an angle of attack

$$\alpha = 18^\mathrm{{o}}$$

and chord based Reynolds number of

$$\mathrm{{Re}}= 3\times 10^4$$

. This study presents experimental data for the forced flow case and recovers the dominant coherent structures and temporal characteristics that describe the evolution of the velocity perturbation. The dominant frequencies are identified by the DMD eigenvalues and the corresponding spatial modes are compared to the dominant POD modes.

Koopman modes are presented for a leading edge separated aerofoil flow with turbulent recirculation. The specific flow configuration is a NACA 0015 aerofoil at an angle of attack of

$$18^\circ $$

18

∘

and a chord based Reynolds number of

$$3\times 10^4$$

3

×

10

4

. This decomposition approximates the evolution of a nonlinear system by a linear operator, the eigenvectors of which represent the spatial form of the fluctuations, and the eigenvalues represent the associated temporal frequencies and growth rates. Proper orthogonal decomposition (POD) modes are used to create a reduced rank linear operator from which the Koopman modes are determined. The sensitivity to the number of POD modes used in the rank reduction is assessed. The dominant frequencies identified by the Koopman eigenvalues coincide with the dominant frequencies determined from a Fourier analysis of probe histories.

The effect on the flow unsteadiness on a NACA 0015 airfoil at Reynolds number

$$Re = 200$$

R

e

=

200

and Angle of Attack

$$AoA = 18^{\circ }$$

A

o

A

=

18

∘

is investigated numerically. Four different geometries based on the NACA 0015 airfoil and with trailing-edge modifications are compared. Long-time integration of the incompressible two-dimensional Navier-Stokes equations shows that the recovered flow field is steady independently of the trailing-edge geometry.

Low Reynolds number airfoils are prone to be adversely affected by the presence of laminar separation bubbles (LSB). But at relatively high Reynolds number (based on the chord of the airfoil) in the range of 100,000–200,000, suppression of LSB, by a boundary layer trip, caused the performance of the airfoil to deteriorate further. In this particular case boundary layer trip does not result in an overall drag reduction due to suppression of the laminar separation bubble, as conventional wisdom would have suggested. The trip causes the turbulent boundary layer to separate early, at relatively high angles of attack, and augmenting the form drag.

Active flow control (AFC) relies on actuators’ control authority as a primary enabling technology for flow manipulation. The requirements of the actuation systems are revisited and tools for

critical

evaluation of actuators are offered. The application in mind is boundary layer separation control. To be accepted by industry, system efficiency should always be assessed, not only the improvement in aerodynamic performance. Clearly there are additional considerations. A few performance based criteria for comparing different actuation concepts are offered, considering the actuation power and system weight. Relevant recent separation control data are compared and discussed.

Airfoil flow separation control using a plasma actuator driven by repetitive nanosecond pulse voltage was experimentally investigated. The pressure distribution on the airfoil surface was measured by means of a liquid manometer. The lift coefficient was computed by integrating the pressure distribution and the effects of the input voltage amplitude and repetitive frequency were evaluated. The results show the lift is increased in two ranges of angle of attack. The first range corresponds to the pre-stall and stall angle of attack. In this range the flow is steady and the lift is increased regardless of the frequency. Strong hysteresis effect is also observed. The second range corresponds to the post-stall angle of attack. In this range the flow is unsteady and the lift increment is heavily dependent on the amplitude and frequency. Characteristic pressure distribution and shift of the separation point, which was estimated from the pressure gradient, are also reported.

Progress toward developing a closed loop control of flow around an airfoil with a Coanda flap is presented. Two loop components were addressed and analysed for the reference no-blowing case: the estimator and its input signal. For the estimator, a Proper Orthogonal Decomposition (POD) Galerkin model based on unsteady Reynolds averaged Navier-Stocks (uRANS) data was evaluated. To compensate for the unresolved dissipative scales in uRANS and for truncation error, the POD Galerkin model was calibrated by introducing an eddy viscosity term. The calibrated POD Galerkin model succeeded in replicating the time coefficients of the first two modes but failed to replicate the higher modes. The sensor location over the flap was optimized using modified Linear Stochastic Estimation (mLSE). With an optimal sensor placement it was possible to determine the state of the flow more accurately than for the same number of evenly spaced sensors.

The experiment was aimed at recovering performance of a thick, turbine blade airfoil degraded due to poor surface quality at Reynolds number of around 500,000. A closed-loop system that controls lift is presented. We used up to three rows of “synthetic jets” coupled with an array of time resolved hot film and pressure sensors to estimate the separation location and lift. Using an amplitude distribution algorithm it was possible to recover the clean turbine blade performance and change the blades lift force as desired over a range of working conditions.

This paper provides an overview of the progress made in a study of the coherent structures of feedback loops found in under-expanded free-jets. In order to gain a better understanding of the topology and dynamics of these structures the proper-orthogonal decomposition (POD) and dynamic mode decomposition (DMD) techniques will be applied to high resolution numerical datasets. We consider a purely convergent under-expanded free jet with nozzle pressure ratios

$${NPR}=\left\{ 2.2,2.6\right\} $$

and a nozzle lip thickness

$$t_n/d=1/3$$

where

$$d=15\,{\text {mm}}$$

is the nozzle diameter. The analysis has shown that DMD is more capable than POD in extracting the structure of instabilities from small datasets which correspond well to the experimental observations.

The linear instability induced by an isolated roughness element in a boundary-layer at Mach 6 has been analysed through spatial BiGlobal and three-dimensional parabolised (PSE-3D) stability analyses. It is important to understand transition in this flow regime since the process can be slower than in incompressible flow and is critical to prediction of local heat loads on next-generation flight vehicles. The results show that the roughness element, with a height of the order of the boundary-layer displacement thickness, generates an convectively unstable wake where different instability modes develop. Furthermore, at this high Mach number, boundary-layer modes develop at high frequencies and are also covered here. Important discrepancies are observed between BiGlobal and PSE-3D predictions, mainly for the roughness-induced wake modes. Results are in qualitative agreement with a full Navier-Stokes receptivity study of the same flow.

The linear global stability of an interaction between an oblique shock wave and a laminar boundary layer is carried out for various oblique shock angles. It is illustrated that such a flow acts as a noise amplifier. The least temporally damped global modes are classified into three main categories, low, medium and high frequencies. The high frequencies are localized into the attached boundary layer, the medium frequencies are associated with Kelvin–Helmholtz like structures along the shear layer and convective waves in the separated flow downstream whereas the low frequencies are driven by the interaction zone. In particular, a low frequency mode emerges which is scaled by the interaction length and the freestream velocity.

Controlling the wake vortex dynamics of bluff bodies efficiently is a fundamental problem in many applications. Earlier direct numerical simulations (Darekar and Sherwin) of three-dimensional bluff bodies demonstrated that the introduction of a spanwise waviness at both the leading and trailing surfaces suppresses the vortex shedding and reduces the amplitude of the fluctuating aerodynamic forces. Under this motivation, starting from a fully developed shedding, a sufficiently high spanwise forcing is introduced on the surface of the cylinder, in the regions where separation effects occur, resulting in the stabilisation of the near wake in a time-independent state, similar to the effect of a sinusoidal stagnation surface. Stability analysis of the linearised Navier-Stokes equations was then performed on the three-dimensional flows to investigate the role of the spanwise modulation on the absolute instability associated with the von Kármán street.

Helical strakes are the most employed devices to mitigate or suppress vortex-induced vibrations of circular cylinders. Although several investigations have been performed in order to predict the performance of these devices, proving its efficiency in specific configurations, little is understood regarding the physical mechanisms leading to the efficiency of these devices. Direct Numerical Simulation and three-dimensional global (TriGlobal) analysis of the flow around a cylinder fitted with helical strakes is performed at low Reynolds number in order to identify and understand more deeply the flow instabilities and physical mechanisms that mitigate and suppress the spanwise-correlated vortex-shedding.

The helical strake is a device commonly employed for vortex-induced vibration attenuation or suppression. It works by changing and affecting the flow patterns around a circular cylinder and, thereby, reducing the interaction of the shear layers formed in this massive separated type of flow. In this paper the wake of vortices generated by a bare circular cylinder is compared to the wake generated by a circular cylinder fitted with helical strake with pitch equal to ten cylinder diameters and height equal to 0.2 of the cylinder diameter. Besides the analysis of the measured velocity field, a Koopman decomposition is made and the most energetic modes obtained for each condition are compared. The Reynolds number for the visualizations is

$$\text {Re} = 10{,}000.$$

Re

=

10

,

000

.

Global instability analysis of the three-dimensional flow past two roughness elements of different shape, namely a cylinder and a bump, is presented. In both cases, the eigenspectrum is made of modes characterised by a varicose symmetry and localised mostly in the zones of large base flow shear. The primary instability exhibited is the same in both cases and consists in an isolated unstable mode probably related to streaks instability. For the cylinder however, a whole branch of modes is in addition destabilised as the Reynolds number is further increased.

Detailed measurements and analysis of temporal and spatial scales inherent in the unsteady asymmetric wake vortex flow generated by a slender axisymmetric body at high angle of attack are performed. Tomographic Particle Image Velocimetry measurements are carried out at

$$40^\circ $$

angle of attack and Reynolds number ranges from

$$1.0\times 10^4$$

to

$$4.5\times 10^4$$

. Results show the presence of two main asymmetric counter rotating vortices. The Reynolds numbers affect the configuration of these vortices where vortex flipping occurred at the lowest Reynolds number investigated. Time-averaged vorticity contours and instantaneous streamlines are presented. Time-averaged vorticity suffered from the expected smoothing of details that have short duration. Instantaneous flow field data such as streamlines shows possible interaction between the main vortices and model attached vortices. Also, the core of the two main vortices can be seen to be affected by the presence of multiple vortex filaments.

A high-frequency periodic jet, issuing parallel to the freestream from immediately below the point of separation, is used to force the turbulent wake of a bluff axisymmetric body. It is shown that, at the optimum jet forcing frequency and momentum flux coefficient, the time-averaged area-weighted base pressure increases by as much as 33 %. A detailed investigation of the effects of forcing is made using modal decomposition of pressure fluctuations on the base of the model and phase-locked two-component PIV. The high-frequency jet creates a row of closely spaced vortices, immediately adjacent to which are regions of large irrotational dissipation on each side. These shear layers inhibit the entrainment of fluid. The resulting pressure recovery is proportional to the strength of the vortices produced by the jet, and is accompanied by a broadband suppression of base pressure fluctuations associated with

all

modes. The optimum forcing frequency, at which amplification of the shear layer approaches unity gain, is roughly five times the shear-layer frequency.

The coherent structures observed in the turbulent wake of axisymmetric bluff bodies are investigated. Concepts from hydrodynamic stability are used to derive low-dimensional mathematical models based on a weakly nonlinear analysis of the governing Navier-Stokes equations that describe the temporal amplitude evolution of the coherent structures in the near wake. Forced experiments applying axisymmetric pulsed-jet blowing on the base of the body are performed to validate the models. Very good quantitative agreement between model predictions and experiments is obtained, showing for the first time that Landau-type models are capable of describing the dynamic behavior of a three-dimensional turbulent wake.

The stability of the near wake of a low aspect ratio cantilevered cylinder, with and without the influence of synthetic jet forcing, was estimated using piecewise two-dimensional inviscid stability analysis. Using a cusp method, the size of the 3-D vortex formation length was estimated. When the synthetic jet was activated it decreased the vortex formation length, altering the spectral content of the near wake, in agreement with experimental measurements. Furthermore, the turbulence intensity within the near wake could be estimated from the eigenfunctions corresponding to the most amplified spatial instability modes.

An experimental study of a 2D square prism with rounded front edges is described. The purpose of the study is to reduce the aerodynamic drag by Active Flow Control (AFC) of boundary layer separation. Robust and efficient suction and pulsed blowing (SaOB) actuators are installed inside a circular cylinder that forms the upper-front curved edge. In addition and for simplicity, steady suction is applied at the lower-front round edge. The AFC results in significant form-drag reduction, narrower wake and correspondingly an increase in the base pressure.

Experiments have been carried out on models of free-to-rotate parallel and oblique plates fitted to a rigid section of circular cylinder to investigate the effect of plate length and oblique angle on the stability of this type of VIV suppressor. Measurements of the dynamic response by trajectories of motion are presented for models with low mass and damping, free to respond in the cross-flow and streamwise directions. It is shown that, depending on a combination of geometric parameters devices might not be able to completely suppress VIV for the whole range of reduced velocities investigated. Plates with larger oblique angles turned to be less stable than parallel plates and induced high-amplitude vibrations for some specific reduced velocities.

A simple way to decrease the drag and oscillating lift forces in the flow around a circular cylinder consists of positioning splitter plates in the wake of the flow. In our work, a geometry consisting of two splitter plates placed close to a circular cylinder was studied. The length of the splitter plates is equal to the cylinder diameter and they are positioned in a side by side configuration parallel to the freestream velocity, with their leading-edges aligned with the cylinder center. This flow was studied using two-dimensional direct numerical simulations, with the Spectral Element Method being employed to solve the incompressible Navier-Stokes equations for Reynolds numbers in the range between 100 and 350. The results showed a strong dependence on the Reynolds number, with the splitter plates being more beneficial at the higher values of Reynolds numbers considered.

Geometries with sudden expansion have been a subject of study for decades now, owing to its engineering applications. While attention has been lavished on flow through symmetric channels with sudden expansion (SE) and backward-facing step (BFS), channels with other divergent angles are studied far less. Straight-diverging-straight (SDS) channels with finite angle of divergences have been studied here. Our focus is on the formation of the laminar separation bubble, typically in the diverging region, and its reattachment downstream. Computations have been carried out to estimate the effect of various parameters such as the angle of divergence

$$(\alpha )$$

, the outlet to intet height ratios

$$(D/d)$$

and the Reynolds numbers

$$(Re)$$

on the formation of the recirculation bubble. The extreme case with

$$\alpha = 90^\circ $$

can be compared to the flow through a symmetric sudden-expansion (SE) flow. The base flow obtained from the two open source codes is characterized for the formation of laminar separation bubble for very low Reynolds numbers

$$(Re)$$

in the parametric space including the angle of divergence,

$$\alpha $$

and the expansion ratio,

$$\kappa =D/d$$

and

$$Re$$

.

The transient dynamics of a high Reynolds number two-dimensional boundary layer flow undergoing a massive separation is investigated. A spanwise array of pulsed round jets, located upstream of the separated region, is used as actuators. Spatial and temporal organisation of the separation and reattachment processes are investigated using phase-averaged PIV measurements in combination with the survey of wall friction along the separation region with the overall objective to develop closed-loop controllers. While different sets of parameters including freestream flow to jet velocities ratio, duty cycle and jets frequency have been considered in the overall work, preliminary results for two cases are presented within.

The objective of this paper is to investigate the effects produced by a dielectric barrier discharge plasma actuator on the separated shear layer flow downstream a backward-facing step. It was highlighted that the electric wind created by the actuator results in an important modification in the flow dynamics when the Strouhal number of the perturbation is equal to 0.25. Then, a lock-on of the vortical flow structures is observed.

Numerical simulations of flow surrounding a synthetic jet actuating device are presented. By modifying a dynamic mesh technique available in OpenFOAM, a well-documented open-source solver for fluid dynamics, detailed computations of the sinusoidal motion of the synthetic jet diaphragm were possible. Numerical solutions were obtained by solving the two dimensional incompressible viscous N–S equations, with the use of a second order implicit time marching scheme and a central finite volume method for spatial discretization in both streamwise and crossflow directions. A systematic parameter study is reported here, in which the external Reynolds number, the diaphragm amplitude and frequency, and the slot dimensions are varied.

The features of the incompressible flow over a rectangular open cavity are studied both numerically, using linear stability analysis, and experimentally in previous works by the authors [

5

,

7

]. Those approaches refer to different states of the flow. The numerical analysis refers to a linear small perturbation superimposed over a two dimensional steady state, while the experimental work studies the complete saturated flow regime, with spanwise walls. Even with such different conditions, both approaches have revealed common features, with the main structures of the experimental flow being recognizable from the corresponding modes of the linear analysis, albeit with certain differences, mainly in the oscillating frequencies [

7

]. The aim of this work is to fill the breach that separates those two states studying the saturation of the flow using a three dimensional non-steady Direct Numerical Simulation (DNS). In this first stage periodic boundary conditions in the spanwise direction will be considered.

A separated flow over an open cavity (Fig.

1

) is primarily characterised by the enhancement of self-sustained oscillations

Accurate reference solutions are very important in stability analysis, where they must act as a reliable base-state. They are also quite useful for unsteady numerical simulations, where they play key roles as initial conditions and in the implementation of boundary conditions, such as buffer zones. Quite often they are approximate solutions for a simplified version of the particular problem at hand, such as boundary-layer solutions. However, these approximate solutions are usually not available, their development is problem dependent and they may not be accurate enough. Hence, there is a need for methodologies that are capable of generating steady-states for arbitrary unsteady differential models. One attempt in this direction is the selective frequency damping technique, despite being developed for problems with a well defined self-excitation frequency. Another attempt to do so is the physical-time damping technique, but temporal dissipation is proportional to the time step. Since numerical instability can keep this time step too small in many nonlinear problems, this technique may not be able to introduce enough dissipation for the damping of all perturbations in very unstable flows. The present work overcomes this problem by noting that optimal damping is not introduced through maximum temporal dissipation, but minimal gain. The implicit Euler scheme employed in the physical-time damping technique achieves both in the limit of infinite CFL numbers, which usually cannot be imposed due to nonlinear effects. This time marching scheme was modified in order for its minimal gain to occur at smaller CFL numbers. Several test cases confirm the efficacy of this new approach.

In this work, the first steps towards developing a continuum-molecular coupled simulation technique are presented, for the purpose of computing macroscopic systems of confined fluids. The idea is to compute the interface wall-fluid by Molecular Dynamics (MD) simulations, where Lennard-Jones potential (and others) have been employed for the molecular interactions, so the usual no slip boundary condition is not specified. Instead, a shear rate can be imposed at the wall, which allows the calculation of wall material properties by means of an iterative method. The remaining fluid region will be computed by a spectral hp method. We present MD simulations of a Couette flow, and the results of the developed boundary conditions from the wall fluid interaction.

Aircraft trailing vortices and their wakes are important to understand in order to shorten the minimum aircraft distances for safe operation in commercial flights. The mechanisms of wake destruction are studied by predictions by both inviscid vortex filament and viscous BiGlobal instability analyses. The two methods have already been applied to the wake problem, but a more detailed comparison is carried out here. The results show excellent agreement between the two methodologies predicting the long wave symmetric instability of a counter-rotating pair of vortices, namely the Crow instability, even at low Reynolds numbers.

Airframe became a relevant source of noise in commercial aircrafts because of the introduction of high by-pass ratio turbofans. The slat is one of the most important airframe noise source, since it represents a source distributed along the wing span. The flow mechanism responsible for noise generation is not completely understood yet. Time-accurate Lattice-Boltzmann simulations were carried out in order to deliver flow data for the calculations of coherent structures in the slat cove by means of the Proper Orthogonal Decomposition (POD) technique. The first two POD-modes are dominated by mixing-layer like structures. Power Spectral Density of the amplitude of these leading POD-functions present the highest level at frequencies that are dominant in the spectrum of far-field acoustic fluctuations.

The purpose is to simulate numerically the flow and noise on the Advanced Noise Control Fan (ANCF). The ANCF model was developed by the NASA Glenn Research Center to provide measurement data of a turbofan flow and its corresponding generated noise. The aim of the numerical simulations is to predict accurately the tonal noise as well as the broadband content of the ducted rotor/stator model using as a reference the provided far-field noise measurements.

Airframe noise is a significant component of the total noise radiated by an aircraft on approach. Although these tones are generated as the result of a complex interaction between the turbulent air flow and the cavity, it is expected that the acoustic resonances of the cavity approach the noise tones at low Mach numbers. Moreover, an accurate design of noise control systems of these cavity tones can be facilitated through an advanced knowledge of the acoustic resonances of the open cavity. The present work presents a computational method to predict the acoustic resonances of a 3D open cavity. A multi-dimensional Helmholtz equation closed with appropriate Perfectly Matched Layer absorbing boundary conditions is solved. Results of the method in the presented three dimensional cavity configuration are shown, the results of which have been compared with experimental measurements in a three-dimensional (cubic) open cavity. Moreover, the noise generated by an electric machine inside of a wind turbine is also studied as direct application of the numerical methodology dealing with very complex geometries.